The present invention relates to a fiber optic gyroscope, and more particularly to a phase modulation fiber optic gyroscope.
Gyroscopes are commonly used for angular velocity sensors for navigational purposes and, for instance, controlling the attitude, etc., of an aircraft or spacecraft. Gyroscopes can also be used for controlling automobiles, robots, etc. A gyroscope allows accurate determination of not only the angular velocity, but also can provide directional data by integrating the former.
A fiber optic gyroscope can be made compact in size because it has no moving parts. Moreover, the fiber optic gyroscope is of especial current interest because it is superior to conventional gyroscopes in characteristics of minimum detectable angular velocity (sensitivity), drift, measurable range (dynamic range), and scale factor stability.
Examples of fiber optic gyroscopes have been described, for instance, by T. G. Giallorenzi and J. A. Bucaro, "Optical Fiber Sensor Technology", IEEE J. of Quantum Electronics, E-18, No. 4, pp. 626-662 (1982); Culshaw and I. P. Giles, "Fiber Optic Gyroscopes", J. Phys. E: Sci. Instrum., 16, pp. 5-15 (1983); and O. Tsubokawa, "Fiber Optic Gyroscope", Study of Lasers, 11, No. 12, pp. 880-902 (1983).
Referring to FIG. 2, the basic principles of a fiber optic gyroscope will be described.
Light received from a luminous element 10 is split by a beam splitter 12 and then inputted to both ends of an optical fiber loop or a sensor coil 20, formed by winding a single mode optical fiber 18 a number of times in the form of a coil, to propagate beams through the sensor coil 20 both clockwise and counterclockwise. If the sensor coil 20 is turning at an angular velocity of .OMEGA., there occurs a phase difference of .DELTA..theta. between the clockwise and counterclockwise beams. The angular velocity .OMEGA. is detected by measuring .DELTA..theta..
The intensity of the electric fields of the beams propagating through the sensor coil 20 clockwise and counterclockwise are represented as follows: EQU E.sub.r =E.sub.1 sin (.omega.t+.DELTA..theta./2) EQU E.sub.l =E.sub.2 sin (.omega.t-.DELTA..theta./2)
where E.sub.1 and E.sub.2 =amplitudes of the counterclockwise and clockwise beams, respectively; .omega.=angular frequency of the beam; t=time; and .DELTA..theta.=phase difference as determined according to the Sagnac effect.
The counterclockwise and clockwise beams with the phase difference .DELTA..theta. therebetween are synthesized by the beam splitter 12 and made incident on the light detecting element 26. The phase difference .DELTA..theta. is detected from the intensities sensed by the light detecting element 26. The phase difference .DELTA..theta. can be expressed by: EQU .DELTA..theta.=(4.pi.La/c.lambda.). .OMEGA. (1)
where L=length of the sensor coil fiber, a=radius of the sensor coil, c=velocity of beam under vacuum, .lambda.=optical wavelength, and .OMEGA.=rotational angular velocity. This is called the Sagnac effect.
Various methods of detecting the phase difference .DELTA..theta. have been proposed. If it is attempted to obtain the sum of the counterclockwise and clockwise beams by means of the light detecting element and square-law detection, the output I is formed as follows: EQU I.alpha.{1+cos (.DELTA..theta.)} (2)
This approach, however, is disadvantageous in that the sensitivity is poor when .DELTA..theta. is close to 0 due to the factor of cos (.DELTA..theta.).
Consequently, there has been proposed an optical mechanism wherein the phase of either counterclockwise or clockwise beam is 90.degree. shifted and subjected to square-law detection. In that case, the output I becomes: EQU I.alpha.{I+sin (.DELTA..theta.)}. (3)
Thus, the sensitivity will be improved when .DELTA..theta. is closer to 0.
However, using this approach, an additional three beam splitters are required to separate the optical paths and thus separate the beams from each other, and also the lengths of the separate optical path must be equal to each other. Therefore, there are difficulties in improving the sensitivity when .DELTA..theta. is close to 0 using the aforementioned static optical detection mechanism.
Various types of fiber optic gyroscopes, specifically, phase modulation and frequency modulation fiber optic gyroscopes, have been proposed wherein dynamic mechanisms are employed to detect .DELTA..theta.. A phase modulation type fiber optic gyroscope surpasses others in terms of the minimum detectable angular velocity.
The phase modulation fiber optic gyroscope is designed to detect the phase difference of .DELTA..theta. by providing a phase modulating element at one end of an optical fiber sensor coil and measuring the intensity of the modulating signal. Referring to FIG. 3, the phase modulation fiber optic gyroscope will be described.
Light capable of interference and received from a luminous element 10 is split into two parts by a beam splitter 12, and the light thus split is introduced to both ends of an optical fiber 18 through coupling lenses 14 and 16. The optical fiber 18 is divided into two portions: one wherein it is wound so as to form a sensor coil 20 and the other 24 wherein it is wound on a phase modulating element 22 such as a piezoelectric element driven at an angular frequency of .omega..sub.m. The beams coupled to respective ends of the optical fiber are propagated through the optical fiber sensor coil 20 clockwise and counterclockwise, emitted from opposite ends thereof, combined by the beam splitter 12, and made incident on a light detecting element 26.
If the positions of the phase modulating element and the sensor coil are arranged asymmetrically, the modulation times will be different from each other although the beams simultaneously emitted from the luminous element are respectively caused to pass through the sensor coil and phase modulating element portions clockwise and counterclockwise. When the output is processed using square-law detection with the light detecting element, the modulating signal will appear in the output. Since .DELTA..theta. is contained in the amplitude of the modulating signal, .DELTA..theta. can be obtained based on the intensity of the modulating signal, which is known.
It is assumed the phase modulator is placed close to the end on which the counterclockwise beam is incident. Given L=the length of the optical fiber sensor coil, n=the reflective index of the fiber core, and the c=the beam velocity, the time .tau. required for the beam to pass through the sensor coil is: EQU .tau.=nL/c (4)
The modulating signal is, as aforementioned, assumed a sine wave having an angular frequency of .omega..sub.m. The light emitted from the luminous element is split into beams propagating clockwise and counterclockwise, and the phase difference .phi. of the modulating signal when each beam is subjected to phase modulation is: ##EQU1##
Due to the Sagnac effect, there is a phase difference of .+-..DELTA..theta./2 between the clockwise and counterclockwise beams, and the phase is further modulated by the phase modulating element. Given b=the amplitude of the phase modulating element, the intensities E.sub.r and E.sub.l of the electric fields of the clockwise and counterclockwise beams are given by: EQU E.sub.r =E.sub.1 sin {.omega.t+.DELTA..theta./2+b. sin (.omega..sub.m t+.phi.)} (6) EQU E.sub.l =E.sub.2 sin {.intg.t-.DELTA..theta./2+b. sin (.omega..sub.m t+.omega.)} (7)
The clockwise and counterclockwise beams having these intensities of electric fields are combined by the beam splitter 12 and processed with square-law detection by the light detecting element 26. Thus the output S(.DELTA..theta.,t) of the light detecting element is made proportional to the product obtained by squaring the sum of E.sub.r and E.sub.l. EQU S(.DELTA..theta.,t)={E.sub.r +E.sub.l }2 (8)
From equation (8): EQU S(.DELTA..theta.,t)=E.sub.1 E.sub.2. cos {.DELTA..theta.+2b. sin (.phi./2). cos (.omega..sub.m t+.phi./2)}+D.C.+{2.omega. or more} (9)
where D.C. designates a d.c. component, and {2.omega. or more} indicates components at least twice as high in angular frequency as the the light signal. Since that value is not detected by detector, however, it is taken as 0.
Thus, .DELTA..theta. is obtained from its relation to the modulating signal because of the phase difference .phi. effected by the phase modulating element.
The term S(.DELTA..theta.,t) can be expanded in a geometric progression using Bessel functions (omitting the D.C. component) as: ##EQU2## From general Bessel function theory: ##EQU3##
By expanding the real and imaginary parts of equation (12) and employing a series expansion of cos and sin terms, portions of equation (10) are obtained.
Provided EQU S(.DELTA..theta.,t)={S.sub.c. cos (.DELTA..theta.)+S.sub.s. sin (.DELTA..theta.)}. E.sub.1 E.sub.2, (13) EQU J.sub.-n (x)=(-1).sup.n J.sub.n (x) (14)
after .theta. is converted into .theta.+.pi./2.
However, if S.sub.c and S.sub.s are written by using the fact that n is a positive number and assuming ##EQU4##
This represents the sum of the series of the fundamental wave of the modulating signal .omega..sub.m and the high frequency signal.
If a suitable filter is used, the fundamental wave .omega..sub.m or a higher harmonic signal of any order can be extracted. Even if such a signal is employed, cos (.DELTA..theta.) or sin (.DELTA..theta.) can be determined. In such a case, the modulation factor imposed by the phase modulating element, the modulation signal angular frequency .omega..sub.m, and the length of time .tau. for the beam to pass through the sensor coil should be set so that the value of the Bessel function J.sub.n (.xi.) of the appropriate order is large.
The highest sensitivity is represented by the first term (n=0) of equation (17), i.e., the second term on the right-hand side of equation (10), which term corresponds to the fundamental wave component.
Assuming the fundamental wave is P(.DELTA..theta.,t), EQU P(.DELTA..theta.,t)=2E.sub.1 E.sub.2.J.sub.1 (.xi.). cos (.omega..sub.m t). sin (.DELTA..theta.) (18)
Accordingly, an output proportional to sin (.DELTA..theta.) is obtained, .DELTA..theta. being obtained from the amplitude of the fundamental wave component.
Moreover, the sensitivity can be further improved if the term .DELTA..theta. in equation (18) is set to maximize J.sub.1 (.xi.). The Bessel function J.sub.1 (.xi.), i.e., the first order term, will be a maximum when .xi.=1.8. The d.c. component J.sub.0 (.xi.) is then almost nearly 0.
The description above refers to the basic construction of a phase modulation fiber optic gyroscope.
As is evident from equation (18), the amplitudes E.sub.1 and E.sub.2 of the clockwise and counterclockwise beams are contained in the fundamental components of the output of the light detecting element. Moreover, there is the coefficient J.sub.1 (.xi.).
For .DELTA..theta. to be correctly obtainable from such an output, the values E.sub.1 and E.sub.2 must be stable. However, those values are in fact variable in the conventional system. Especially the amplitudes of E.sub.1 and E.sub.2 are subject to variation. More specifically, E.sub.1 and E.sub.2 readily change with the output of the luminous element and the quantity of light passing through the polarizer used to eliminate differences in the light paths or shifts in the position of the optical system. For these reasons, the scale factor of the output of a phase modulation fiber optic gyroscope is generally quite unstable, varying by up to 100% for a conventional signal mode optical fiber.
On the other hand, such variations can be substantially controlled by the introduction of a constant polarizing fiber to determine the direction at which light is incident on the fiber. However, the existing constant polarizing fiber poses problems in terms of the temperature characteristics in the coefficient of extinction. That is, the polarizing state fluctuates with temperature, pressure and distortion while the beams propagate through the fiber, causing the amplitudes E.sub.1 and E.sub.2 of the light reaching the luminous element and the scale factor to fluctuate by on the order of 15 to 30%.
Consequently, attempts have been to correct for this problem whereby the amplitudes of E.sub.1 and E.sub.2 are monitored. In such a fiber optic gyroscope, beam splitters are inserted in each of the clockwise and counterclockwise light paths so as to extract portions of the respective light beams and thereby measure the amplitude of E.sub.1 and E.sub.2. Although this approach may be successful in that the outputs are stabilized, the resulting construction has disadvantages in that the number of parts is increased and in that the quantity of light reaching the light detecting element is reduced, thereby causing a reduction in the S/N ratio.
In order to overcome these problems, the present inventor has devised a method for detecting the d.c. component while the light detecting element is actuated and obtaining sin (.DELTA..theta.) or cos (.DELTA..theta.) by dividing the output of the gyroscope by the d.c. component. However, there has occurred a problem that the S/N ratio is reduced due to a reduced quantity of light reaching the light detecting element.